def test_arch_lm(simulated_data):
zm = ZeroMean(simulated_data, volatility=GARCH())
res = zm.fit(disp=DISPLAY)
wald = res.arch_lm_test()
nobs = simulated_data.shape[0]
df = int(np.ceil(12.0 * np.power(nobs / 100.0, 1 / 4.0)))
assert wald.df == df
assert "Standardized" not in wald.null
assert "Standardized" not in wald.alternative
assert "H0: Standardized" not in wald.__repr__()
assert "heteroskedastic" in wald.__repr__()
resids2 = pd.Series(res.resid ** 2)
data = [resids2.shift(i) for i in range(df + 1)]
data = pd.concat(data, 1).dropna()
lhs = data.iloc[:, 0]
rhs = smtools.add_constant(data.iloc[:, 1:])
ols_res = smlm.OLS(lhs, rhs).fit()
assert_almost_equal(wald.stat, nobs * ols_res.rsquared)
assert len(wald.critical_values) == 3
assert "10%" in wald.critical_values
wald = res.arch_lm_test(lags=5)
assert wald.df == 5
assert_almost_equal(wald.pval, 1 - stats.chi2(5).cdf(wald.stat))
wald = res.arch_lm_test(standardized=True)
assert wald.df == df
assert "Standardized" in wald.null
assert "Standardized" in wald.alternative
assert_almost_equal(wald.pval, 1 - stats.chi2(df).cdf(wald.stat))
assert "H0: Standardized" in wald.__repr__()
def test_zero_mean(self):
zm = ZeroMean(self.y)
parameters = np.array([1.0])
data = zm.simulate(parameters, self.T)
assert_equal(data.shape, (self.T, 3))
assert_equal(data['data'].shape[0], self.T)
assert_equal(zm.num_params, 0)
bounds = zm.bounds()
assert_equal(bounds, [])
assert_equal(zm.constant, False)
a, b = zm.constraints()
assert_equal(a, np.empty((0, 0)))
assert_equal(b, np.empty((0, )))
assert isinstance(zm.volatility, ConstantVariance)
assert isinstance(zm.distribution, Normal)
assert_equal(zm.lags, None)
res = zm.fit(disp='off')
assert_almost_equal(res.params, np.array([np.mean(self.y**2)]))
forecasts = res.forecast(horizon=99)
direct = pd.DataFrame(
index=np.arange(self.y.shape[0]),
columns=['h.{0:>02d}'.format(i + 1) for i in range(99)],
dtype=np.float64)
direct.iloc[:, :] = 0.0
assert isinstance(forecasts, ARCHModelForecast)
# TODO
# assert_frame_equal(direct, forecasts)
garch = GARCH()
zm.volatility = garch
zm.fit(update_freq=0, disp=DISPLAY)
def test_backcast_error(simulated_data):
zm = ZeroMean(simulated_data, volatility=GARCH())
with pytest.raises(ValueError):
zm.fit(backcast=-1, disp=DISPLAY)
zm = ZeroMean(simulated_data, volatility=RiskMetrics2006())
with pytest.raises(ValueError):
zm.fit(backcast=np.ones(100), disp=DISPLAY)
def test_zero_mean(self):
zm = ZeroMean(self.y)
parameters = np.array([1.0])
data = zm.simulate(parameters, self.T)
assert_equal(data.shape, (self.T, 3))
assert_equal(data['data'].shape[0], self.T)
assert_equal(zm.num_params, 0)
bounds = zm.bounds()
assert_equal(bounds, [])
assert_equal(zm.constant, False)
a, b = zm.constraints()
assert_equal(a, np.empty((0, 0)))
assert_equal(b, np.empty((0,)))
assert isinstance(zm.volatility, ConstantVariance)
assert isinstance(zm.distribution, Normal)
assert_equal(zm.lags, None)
res = zm.fit(disp='off')
assert_almost_equal(res.params, np.array([np.mean(self.y ** 2)]))
forecasts = res.forecast(horizon=99)
direct = pd.DataFrame(index=np.arange(self.y.shape[0]),
columns=['h.{0:>02d}'.format(i + 1) for i in
range(99)],
dtype=np.float64)
direct.iloc[:, :] = 0.0
assert isinstance(forecasts, ARCHModelForecast)
# TODO
# assert_frame_equal(direct, forecasts)
garch = GARCH()
zm.volatility = garch
zm.fit(update_freq=0, disp=DISPLAY)
def setup_class(cls):
cls.rng = RandomState(1234)
cls.T = 1000
cls.resids = cls.rng.standard_normal(cls.T)
zm = ZeroMean()
zm.volatility = GARCH()
seed = 12345
random_state = np.random.RandomState(seed)
zm.distribution = Normal(random_state=random_state)
sim_data = zm.simulate(np.array([0.1, 0.1, 0.8]), 1000)
with pytest.raises(ValueError):
zm.simulate(np.array([0.1, 0.1, 0.8]), 1000, initial_value=3.0)
date_index = pd.date_range("2000-12-31", periods=1000, freq="W")
cls.y = sim_data.data.values
cls.y_df = pd.DataFrame(
cls.y[:, None], columns=["LongVariableName"], index=date_index
)
cls.y_series = pd.Series(
cls.y, name="VeryVeryLongLongVariableName", index=date_index
)
x = cls.resids + cls.rng.standard_normal(cls.T)
cls.x = x[:, None]
cls.x_df = pd.DataFrame(cls.x, columns=["LongExogenousName"])
cls.resid_var = np.var(cls.resids)
cls.sigma2 = np.zeros_like(cls.resids)
cls.backcast = 1.0
def test_empty_mean(self):
mod = HARX(self.y, None, None, False, volatility=ConstantVariance(),
distribution=Normal())
res = mod.fit()
mod = ZeroMean(self.y, volatility=ConstantVariance(), distribution=Normal())
res_z = mod.fit()
assert res.num_params == res_z.num_params
assert_series_equal(res.params, res_z.params)
assert res.loglikelihood == res_z.loglikelihood
def setup_class(cls):
cls.rng = RandomState(1234)
cls.T = 1000
cls.resids = cls.rng.randn(cls.T)
zm = ZeroMean()
zm.volatility = GARCH()
sim_data = zm.simulate(np.array([0.1, 0.1, 0.8]), 1000)
date_index = pd.date_range('2000-12-31', periods=1000, freq='W')
cls.y = sim_data.data.values
cls.y_df = pd.DataFrame(cls.y[:, None],
columns=['LongVariableName'],
index=date_index)
cls.y_series = pd.Series(cls.y,
name='VeryVeryLongLongVariableName',
index=date_index)
x = cls.resids + cls.rng.randn(cls.T)
cls.x = x[:, None]
cls.x_df = pd.DataFrame(cls.x, columns=['LongExogenousName'])
cls.resid_var = np.var(cls.resids)
cls.sigma2 = np.zeros_like(cls.resids)
cls.backcast = 1.0
def setup_class(cls):
np.random.seed(1234)
cls.T = 1000
cls.resids = randn(cls.T)
np.random.seed(1234)
zm = ZeroMean()
zm.volatility = GARCH()
sim_data = zm.simulate(np.array([0.1, 0.1, 0.8]), 1000)
date_index = pd.date_range('2000-12-31', periods=1000, freq='W')
cls.y = sim_data.data.values
cls.y_df = pd.DataFrame(cls.y[:, None],
columns=['LongVariableName'],
index=date_index)
cls.y_series = pd.Series(cls.y,
name='VeryVeryLongLongVariableName',
index=date_index)
x = cls.resids + randn(cls.T)
cls.x = x[:, None]
cls.x_df = pd.DataFrame(cls.x, columns=['LongExogenousName'])
cls.resid_var = np.var(cls.resids)
cls.sigma2 = np.zeros_like(cls.resids)
cls.backcast = 1.0
def test_backcast(volatility, simulated_data):
zm = ZeroMean(simulated_data, volatility=volatility())
res = zm.fit(disp=DISPLAY)
bc = zm.volatility.backcast(np.asarray(res.resid))
if volatility is EGARCH:
bc = np.exp(bc)
res2 = zm.fit(backcast=bc, disp=DISPLAY)
assert_array_almost_equal(res.params, res2.params)
if volatility is RiskMetrics2006:
zm.fit(backcast=bc[0], disp=DISPLAY)
def simulated_data(request):
rs = np.random.RandomState(1)
zm = ZeroMean(volatility=GARCH(), distribution=Normal(rs))
sim_data = zm.simulate(np.array([0.1, 0.1, 0.88]), 1000)
return np.asarray(sim_data.data) if request.param else sim_data.data
def test_fit_smoke(simulated_data, volatility):
zm = ZeroMean(simulated_data, volatility=volatility())
zm.fit(disp=DISPLAY)
def simulated_data():
rs = np.random.RandomState(1)
zm = ZeroMean(volatility=GARCH(), distribution=Normal(rs))
sim_data = zm.simulate(np.array([0.1, 0.1, 0.88]), 1000)
return sim_data.data
def test_parameterless_fit(first_obs, last_obs, vol):
base = ConstantMean(SP500, volatility=vol)
base_res = base.fit(first_obs=first_obs, last_obs=last_obs, disp="off")
mod = ZeroMean(SP500, volatility=vol)
res = mod.fit(first_obs=first_obs, last_obs=last_obs, disp="off")
assert res.conditional_volatility.shape == base_res.conditional_volatility.shape